We extend earlier work on the nonlinear behavior of premixed flames in a gravitationally stratified medium, subject to the Boussinesq approximation, in two dimensions. The main result is that the nature of the traveling burning front is largely determined by the form of the adopted boundary conditions on the side walls: while symmetric boundary conditions lead to stably scalloped traveling wave...

The dynamics of spectral transport in two-dimensional turbulent convection of electrically conducting fluids is studied by means of direct numerical simulations in the frame of the magnetohydrodynamic Boussinesq approximation. The system performs quasioscillations between two different regimes of small-scale turbulence: one dominated by nonlinear magnetohydrodynamic interactions; the other gove...

It is shown that the anelastic Oberbeck-Boussinesq system is a small Mach, small Péclet and small Froude number limit of the complete Navier-Stokes-Fourier system for gases with large specific heat at constant volume. This result is obtained on an arbitrary large time interval. The proof allows an intrinsic view into the process of separation of fast oscillating acoustic waves, governed by a Li...

A numerical study of Rayleigh-Benard convection in an infinite fluid layer (Pr=0.71) is performed using large eddy simulation (LES) of the Navier-Stokes equations with the Boussinesq approximation. We present results in the ’hard turbulence’ regime (2.10 < Ra < 2.10). The LES modelling uses the mixed scale diffusivity model, that we have originally developed in the case of the differentially he...

We investigate the nature of entropy generation for natural convection in a twodimensional square section enclosure vibrating sinusoidally perpendicular to the applied temperature gradient in a zero-gravity field. The enclosure is assumed to fill with porous media. The Darcy momentum equation is used to model the porous media. The full governing differential equations are simplified with the Bo...

We consider the Maxey-Riley equation for small neutrally buoyant inertial particles in Boussinesq approximation. The main motivation is study of phytoplankton and oceanic turbulent flows. show that behave as forced damped oscillators, with different regimes depending on Stokes number fluid Brunt-V\"ais\"al\"a frequency. Using direct numerical simulations we their dynamics these flows tend to cl...

We show that the semi-implicit time discretization approaches previously introduced for multilayer shallow water models barotropic case can be also applied to variable density with Boussinesq approximation. Furthermore, equations, a number of layers used, so as achieve greater flexibility and efficiency resulting approach. An analysis linearized system, which allows derive linear stability para...

Based on the homotopy perturbation method (HPM) and Padé approximants (PA), approximate and exact solutions are obtained for cubic Boussinesq and modified Boussinesq equations. The obtained solutions contain solitary waves, rational solutions. HPM is used for analytic treatment to those equations and PA for increasing the convergence region of the HPM analytical solution. The results reveal tha...

The incompressible Boussinesq equations not only have many applications in modeling fluids and geophysical fluids but also are mathematically important. The well-posedness and related problem on the Boussinesq equations have recently attracted considerable interest. This paper examines the global regularity issue on the 2D Boussinesq equations with fractional Laplacian dissipation and thermal d...

Most models of astrophysical flows employ a ``sound-proof'' approximation, such as the Boussinesq, anelastic, and pseudo-incompressible models, which remove acoustic waves from governing equations. Here, we address accuracy each these for describing magnetic buoyancy in solar interior. We introduce general sound-proof model compare its behavior to that fully compressible system within range ast...